Merging vertices at the center point when using a mirror modifier?
On the modifier properties there is a checkbox called Clipping (shown as 1 in the image bellow), it will merge the vertex as it touch the edge (prevent vertices from going through the mirror during transform).

Note: If you're not seeing the vertex because it's hidden by faces and you can't select it, you can turn off the modifier visualization (the eye icon button from 2 in the image bellow), there's also a button with the "triangle vertex" that allow you edit from the reflection too. Also, at the bottom of 3D view in the vertex selection options, there is a button with a "wire cube" that allow you to see and edit vertex though the faces.